%I #16 Mar 13 2021 11:03:39

%S 2,5,6,20,28,48,170,274,350,1670,2731,3350,16670,27274,33350,166670,

%T 272731,333350,1666670,2727274,3333350,16666670,27272731,33333350,

%U 166666670

%N Records in A341755 (= length of chain of (k,k+1) sharing a digit with k+(k+1), starting at n).

%C The indices of these records, i.e., k such that a(n) = A341755(k) > A341755(m) for all m < k, are listed in A341757.

%F a(n) = A341755(A341757(n)).

%F Conjecture: | a(n+3)/10 - a(n) | <= 10 for all n except n = 6; specifically:

%F a(3n+6) = 3...350 with n '3's, n >= 1;

%F a(3n+7) = 16...670 with n '6's, n >= 0.

%e After {0, 1}, the first nontrivial chain is {9, 10, 11, 12, 13} with 5 members.

%e The chain of length 48 starting at 486 contains a somewhat "trivial" chain starting at 500: the shared digit of the first 10 terms is the '0' of 10** and 50*, the shared digit of the next 10-11 terms is the '1' of 10** and 51*.

%o (PARI) lista(nn) = my(m, t); for(k=0, nn, if(t=A341755(k), if(t>m, print1(m=t, ", ")); k+=t-1)) \\ modified by _Jinyuan Wang_, Mar 13 2021

%Y Cf. A341755, A341757.

%K nonn,base,more

%O 1,1

%A _M. F. Hasler_, Mar 01 2021

%E a(14)-a(25) from _Jinyuan Wang_, Mar 13 2021